- Well-ordering theorem (Wikipedia)
In mathematics, the well-ordering theorem, also known as Zermelo’s theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. The well-ordering theorem together with Zorn’s lemma are the most important mathematical statements that are equivalent to the axiom of choice (often called AC, see also Axiom of choice § Equivalents). Ernst Zermelo introduced the axiom of choice as an “unobjectionable logical principle” to prove the well-ordering theorem. One can conclude from the well-ordering theorem that every set is susceptible to transfinite induction, which is considered by mathematicians to be a powerful technique. One famous consequence of the theorem is the Banach–Tarski paradox.
setting in a movie but filmed in Vancouver
- Vancouver Never Plays Itself (YouTube)
Perhaps no other city has been as thoroughly hidden from modern filmmaking as Vancouver, my hometown. Today, it’s the third biggest film production city in North America, behind Los Angeles and New York. And yet for all the movies and TV shows that are shot there, we hardly ever see the city itself. So today, let’s focus less on the movies and more on the city in the background.
- Santa Barbara, California (Wikipedia)
Santa Barbara (Spanish: Santa Bárbara, meaning ‘Saint Barbara’) is a coastal city in Santa Barbara County, California, of which it is also the county seat. Situated on a south-facing section of coastline, the longest such section on the West Coast of the United States, the city lies between the steeply rising Santa Ynez Mountains and the Pacific Ocean. Santa Barbara’s climate is often described as Mediterranean, and the city has been dubbed “The American Riviera”. According to the 2020 U.S. Census, the city’s population was 88,665.
